Pandas Profiling Report

Dataset statistics

Number of variables	9
Number of observations	1030
Missing cells	0
Missing cells (%)	0.0%
Duplicate rows	25
Duplicate rows (%)	2.4%
Total size in memory	72.5 KiB
Average record size in memory	72.1 B

Variable types

NUM	9

Reproduction

Analysis started	2020-10-30 23:41:18.432079
Analysis finished	2020-10-30 23:41:31.388782
Duration	12.96 seconds
Version	pandas-profiling v2.8.0
Command line	`pandas_profiling --config_file config.yaml [YOUR_FILE.csv]`
Download configuration	config.yaml

Warnings

Dataset has 25 (2.4%) duplicate rows	Duplicates
`slag` has 471 (45.7%) zeros	Zeros
`ash` has 566 (55.0%) zeros	Zeros
`superplastic` has 379 (36.8%) zeros	Zeros

cement
Real number (ℝ_≥0)

Distinct count	278
Unique (%)	27.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	281.16786407766995
Minimum	102.0
Maximum	540.0
Zeros	0
Zeros (%)	0.0%
Memory size	8.0 KiB

Quantile statistics

Minimum	102
5-th percentile	143.745
Q1	192.375
median	272.9
Q3	350
95-th percentile	480
Maximum	540
Range	438
Interquartile range (IQR)	157.625

Descriptive statistics

Standard deviation	104.5063645
Coefficient of variation (CV)	0.3716867318
Kurtosis	-0.5206522845
Mean	281.1678641
Median Absolute Deviation (MAD)	79.4
Skewness	0.5094811789
Sum	289602.9
Variance	10921.58022

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
425	20	1.9%
362.6	20	1.9%
251.4	15	1.5%
446	14	1.4%
310	14	1.4%
475	13	1.3%
331	13	1.3%
250	13	1.3%
387	12	1.2%
349	12	1.2%
Other values (268)	884	85.8%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
102	4	0.4%
108.3	4	0.4%
116	4	0.4%
122.6	4	0.4%
132	2	0.2%

Value	Count	Frequency (%)
540	9	0.9%
531.3	5	0.5%
528	1	0.1%
525	7	0.7%
522	2	0.2%

slag
Real number (ℝ_≥0)

ZEROS

Distinct count	185
Unique (%)	18.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	73.89582524271844
Minimum	0.0
Maximum	359.4
Zeros	471
Zeros (%)	45.7%
Memory size	8.0 KiB

Quantile statistics

Minimum	0
5-th percentile	0
Q1	0
median	22
Q3	142.95
95-th percentile	236
Maximum	359.4
Range	359.4
Interquartile range (IQR)	142.95

Descriptive statistics

Standard deviation	86.27934175
Coefficient of variation (CV)	1.167580732
Kurtosis	-0.5081754789
Mean	73.89582524
Median Absolute Deviation (MAD)	22
Skewness	0.8007168956
Sum	76112.7
Variance	7444.124812

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
0	471	45.7%
189	30	2.9%
106.3	20	1.9%
24	14	1.4%
20	12	1.2%
145	11	1.1%
19	10	1.0%
98.1	10	1.0%
22	8	0.8%
26	8	0.8%
Other values (175)	436	42.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	471	45.7%
11	4	0.4%
13.6	5	0.5%
15	5	0.5%
17.2	1	0.1%

Value	Count	Frequency (%)
359.4	2	0.2%
342.1	2	0.2%
316.1	2	0.2%
305.3	4	0.4%
290.2	2	0.2%

ash
Real number (ℝ_≥0)

ZEROS

Distinct count	156
Unique (%)	15.1%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	54.18834951456311
Minimum	0.0
Maximum	200.1
Zeros	566
Zeros (%)	55.0%
Memory size	8.0 KiB

Quantile statistics

Minimum	0
5-th percentile	0
Q1	0
median	0
Q3	118.3
95-th percentile	167
Maximum	200.1
Range	200.1
Interquartile range (IQR)	118.3

Descriptive statistics

Standard deviation	63.99700415
Coefficient of variation (CV)	1.181010397
Kurtosis	-1.328746435
Mean	54.18834951
Median Absolute Deviation (MAD)	0
Skewness	0.5373539058
Sum	55814
Variance	4095.616541

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
0	566	55.0%
118.3	20	1.9%
141	16	1.6%
24.5	15	1.5%
79	14	1.4%
94	13	1.3%
100.4	11	1.1%
100.5	10	1.0%
98.8	10	1.0%
174.2	10	1.0%
Other values (146)	345	33.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	566	55.0%
24.5	15	1.5%
59	1	0.1%
60	1	0.1%
71	1	0.1%

Value	Count	Frequency (%)
200.1	1	0.1%
200	1	0.1%
195	3	0.3%
194.9	1	0.1%
194	1	0.1%

water
Real number (ℝ_≥0)

Distinct count	195
Unique (%)	18.9%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	181.56728155339806
Minimum	121.8
Maximum	247.0
Zeros	0
Zeros (%)	0.0%
Memory size	8.0 KiB

Quantile statistics

Minimum	121.8
5-th percentile	146.1
Q1	164.9
median	185
Q3	192
95-th percentile	228
Maximum	247
Range	125.2
Interquartile range (IQR)	27.1

Descriptive statistics

Standard deviation	21.35421857
Coefficient of variation (CV)	0.1176104989
Kurtosis	0.1220816744
Mean	181.5672816
Median Absolute Deviation (MAD)	13
Skewness	0.07462838429
Sum	187014.3
Variance	456.0026505

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
192	118	11.5%
228	54	5.2%
185.7	46	4.5%
203.5	36	3.5%
186	28	2.7%
162	20	1.9%
164.9	20	1.9%
153.5	15	1.5%
185	15	1.5%
178	14	1.4%
Other values (185)	664	64.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
121.8	5	0.5%
126.6	5	0.5%
127	1	0.1%
127.3	1	0.1%
137.8	5	0.5%

Value	Count	Frequency (%)
247	1	0.1%
246.9	1	0.1%
237	1	0.1%
236.7	1	0.1%
228	54	5.2%

superplastic
Real number (ℝ_≥0)

ZEROS

Distinct count	111
Unique (%)	10.8%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	6.204660194174758
Minimum	0.0
Maximum	32.2
Zeros	379
Zeros (%)	36.8%
Memory size	8.0 KiB

Quantile statistics

Minimum	0
5-th percentile	0
Q1	0
median	6.4
Q3	10.2
95-th percentile	16.055
Maximum	32.2
Range	32.2
Interquartile range (IQR)	10.2

Descriptive statistics

Standard deviation	5.973841392
Coefficient of variation (CV)	0.9627991228
Kurtosis	1.411268965
Mean	6.204660194
Median Absolute Deviation (MAD)	5.3
Skewness	0.9072025749
Sum	6390.8
Variance	35.68678098

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
0	379	36.8%
11.6	37	3.6%
8	27	2.6%
7	19	1.8%
6	17	1.7%
9	16	1.6%
8.9	16	1.6%
7.8	16	1.6%
9.9	16	1.6%
10	15	1.5%
Other values (101)	472	45.8%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
0	379	36.8%
1.7	4	0.4%
1.9	1	0.1%
2	1	0.1%
2.2	1	0.1%

Value	Count	Frequency (%)
32.2	5	0.5%
28.2	5	0.5%
23.4	5	0.5%
22.1	1	0.1%
22	6	0.6%

coarseagg
Real number (ℝ_≥0)

Distinct count	284
Unique (%)	27.6%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	972.9189320388349
Minimum	801.0
Maximum	1145.0
Zeros	0
Zeros (%)	0.0%
Memory size	8.0 KiB

Quantile statistics

Minimum	801
5-th percentile	842
Q1	932
median	968
Q3	1029.4
95-th percentile	1104
Maximum	1145
Range	344
Interquartile range (IQR)	97.4

Descriptive statistics

Standard deviation	77.75395397
Coefficient of variation (CV)	0.07991822485
Kurtosis	-0.5990161032
Mean	972.918932
Median Absolute Deviation (MAD)	46.3
Skewness	-0.04021974481
Sum	1002106.5
Variance	6045.677357

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
932	57	5.5%
852.1	45	4.4%
944.7	30	2.9%
968	29	2.8%
1125	24	2.3%
967	19	1.8%
1047	19	1.8%
974	12	1.2%
942	12	1.2%
822	12	1.2%
Other values (274)	771	74.9%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
801	4	0.4%
801.1	1	0.1%
801.4	1	0.1%
811	2	0.2%
814	1	0.1%

Value	Count	Frequency (%)
1145	1	0.1%
1134.3	5	0.5%
1130	1	0.1%
1125	24	2.3%
1124.4	2	0.2%

fineagg
Real number (ℝ_≥0)

Distinct count	302
Unique (%)	29.3%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	773.5804854368931
Minimum	594.0
Maximum	992.6
Zeros	0
Zeros (%)	0.0%
Memory size	8.0 KiB

Quantile statistics

Minimum	594
5-th percentile	613
Q1	730.95
median	779.5
Q3	824
95-th percentile	898.09
Maximum	992.6
Range	398.6
Interquartile range (IQR)	93.05

Descriptive statistics

Standard deviation	80.17598014
Coefficient of variation (CV)	0.1036427129
Kurtosis	-0.1021769893
Mean	773.5804854
Median Absolute Deviation (MAD)	45.5
Skewness	-0.2530095977
Sum	796787.9
Variance	6428.187792

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
594	30	2.9%
755.8	30	2.9%
670	23	2.2%
613	22	2.1%
801	16	1.6%
887.1	15	1.5%
746.6	15	1.5%
845	14	1.4%
712	14	1.4%
750	12	1.2%
Other values (292)	839	81.5%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
594	30	2.9%
605	5	0.5%
611.8	5	0.5%
612	1	0.1%
613	22	2.1%

Value	Count	Frequency (%)
992.6	5	0.5%
945	4	0.4%
943.1	4	0.4%
942	4	0.4%
925.7	5	0.5%

age
Real number (ℝ_≥0)

Distinct count	14
Unique (%)	1.4%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	45.662135922330094
Minimum	1
Maximum	365
Zeros	0
Zeros (%)	0.0%
Memory size	8.0 KiB

Quantile statistics

Minimum	1
5-th percentile	3
Q1	7
median	28
Q3	56
95-th percentile	180
Maximum	365
Range	364
Interquartile range (IQR)	49

Descriptive statistics

Standard deviation	63.16991158
Coefficient of variation (CV)	1.383419989
Kurtosis	12.16898898
Mean	45.66213592
Median Absolute Deviation (MAD)	21
Skewness	3.269177401
Sum	47032
Variance	3990.437729

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
28	425	41.3%
3	134	13.0%
7	126	12.2%
56	91	8.8%
14	62	6.0%
90	54	5.2%
100	52	5.0%
180	26	2.5%
91	22	2.1%
365	14	1.4%
Other values (4)	24	2.3%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
1	2	0.2%
3	134	13.0%
7	126	12.2%
14	62	6.0%
28	425	41.3%

Value	Count	Frequency (%)
365	14	1.4%
360	6	0.6%
270	13	1.3%
180	26	2.5%
120	3	0.3%

strength
Real number (ℝ_≥0)

Distinct count	845
Unique (%)	82.0%
Missing	0
Missing (%)	0.0%
Infinite	0
Infinite (%)	0.0%

Mean	35.817961165048544
Minimum	2.33
Maximum	82.6
Zeros	0
Zeros (%)	0.0%
Memory size	8.0 KiB

Quantile statistics

Minimum	2.33
5-th percentile	10.961
Q1	23.71
median	34.445
Q3	46.135
95-th percentile	66.802
Maximum	82.6
Range	80.27
Interquartile range (IQR)	22.425

Descriptive statistics

Standard deviation	16.70574196
Coefficient of variation (CV)	0.4664068366
Kurtosis	-0.3137248604
Mean	35.81796117
Median Absolute Deviation (MAD)	10.93
Skewness	0.4169772884
Sum	36892.5
Variance	279.0818145

Histogram

Histogram with fixed size bins (bins=10)

Value	Count	Frequency (%)
33.4	6	0.6%
79.3	4	0.4%
41.05	4	0.4%
71.3	4	0.4%
35.3	4	0.4%
23.52	4	0.4%
31.35	4	0.4%
77.3	4	0.4%
37.27	3	0.3%
55.9	3	0.3%
Other values (835)	990	96.1%

Minimum 5 values
Maximum 5 values

Value	Count	Frequency (%)
2.33	1	0.1%
3.32	1	0.1%
4.57	1	0.1%
4.78	1	0.1%
4.83	1	0.1%

Value	Count	Frequency (%)
82.6	1	0.1%
81.75	1	0.1%
80.2	1	0.1%
79.99	1	0.1%
79.4	1	0.1%

Pearson's r

The Pearson's correlation coefficient (r) is a measure of linear correlation between two variables. It's value lies between -1 and +1, -1 indicating total negative linear correlation, 0 indicating no linear correlation and 1 indicating total positive linear correlation. Furthermore, r is invariant under separate changes in location and scale of the two variables, implying that for a linear function the angle to the x-axis does not affect r.

To calculate r for two variables X and Y, one divides the covariance of X and Y by the product of their standard deviations.

Spearman's ρ

The Spearman's rank correlation coefficient (ρ) is a measure of monotonic correlation between two variables, and is therefore better in catching nonlinear monotonic correlations than Pearson's r. It's value lies between -1 and +1, -1 indicating total negative monotonic correlation, 0 indicating no monotonic correlation and 1 indicating total positive monotonic correlation.

To calculate ρ for two variables X and Y, one divides the covariance of the rank variables of X and Y by the product of their standard deviations.

Kendall's τ

Similarly to Spearman's rank correlation coefficient, the Kendall rank correlation coefficient (τ) measures ordinal association between two variables. It's value lies between -1 and +1, -1 indicating total negative correlation, 0 indicating no correlation and 1 indicating total positive correlation.

To calculate τ for two variables X and Y, one determines the number of concordant and discordant pairs of observations. τ is given by the number of concordant pairs minus the discordant pairs divided by the total number of pairs.

Phik (φk)

Phik (φk) is a new and practical correlation coefficient that works consistently between categorical, ordinal and interval variables, captures non-linear dependency and reverts to the Pearson correlation coefficient in case of a bivariate normal input distribution. There is extensive documentation available here.

Count
Matrix

First rows

	cement	slag	ash	water	superplastic	coarseagg	fineagg	age	strength
0	141.3	212.0	0.0	203.5	0.0	971.8	748.5	28	29.89
1	168.9	42.2	124.3	158.3	10.8	1080.8	796.2	14	23.51
2	250.0	0.0	95.7	187.4	5.5	956.9	861.2	28	29.22
3	266.0	114.0	0.0	228.0	0.0	932.0	670.0	28	45.85
4	154.8	183.4	0.0	193.3	9.1	1047.4	696.7	28	18.29
5	255.0	0.0	0.0	192.0	0.0	889.8	945.0	90	21.86
6	166.8	250.2	0.0	203.5	0.0	975.6	692.6	7	15.75
7	251.4	0.0	118.3	188.5	6.4	1028.4	757.7	56	36.64
8	296.0	0.0	0.0	192.0	0.0	1085.0	765.0	28	21.65
9	155.0	184.0	143.0	194.0	9.0	880.0	699.0	28	28.99

Last rows

	cement	slag	ash	water	superplastic	coarseagg	fineagg	age	strength
1020	183.9	122.6	0.0	203.5	0.0	959.2	800.0	7	10.79
1021	203.5	305.3	0.0	203.5	0.0	963.4	630.0	3	9.56
1022	144.8	0.0	133.6	180.8	11.1	979.5	811.5	28	13.20
1023	141.3	212.0	0.0	203.5	0.0	971.8	748.5	7	10.39
1024	297.2	0.0	117.5	174.8	9.5	1022.8	753.5	3	21.91
1025	135.0	0.0	166.0	180.0	10.0	961.0	805.0	28	13.29
1026	531.3	0.0	0.0	141.8	28.2	852.1	893.7	3	41.30
1027	276.4	116.0	90.3	179.6	8.9	870.1	768.3	28	44.28
1028	342.0	38.0	0.0	228.0	0.0	932.0	670.0	270	55.06
1029	540.0	0.0	0.0	173.0	0.0	1125.0	613.0	7	52.61

Most frequent

	cement	slag	water	superplastic	coarseagg	fineagg	age	strength	count
1	362.6	189.0	164.9	11.6	944.7	755.8	3	35.30	4
3	362.6	189.0	164.9	11.6	944.7	755.8	28	71.30	4
4	362.6	189.0	164.9	11.6	944.7	755.8	56	77.30	4
5	362.6	189.0	164.9	11.6	944.7	755.8	91	79.30	4
2	362.6	189.0	164.9	11.6	944.7	755.8	7	55.90	3
6	425.0	106.3	153.5	16.5	852.1	887.1	3	33.40	3
7	425.0	106.3	153.5	16.5	852.1	887.1	7	49.20	3
8	425.0	106.3	153.5	16.5	852.1	887.1	28	60.29	3
9	425.0	106.3	153.5	16.5	852.1	887.1	56	64.30	3
10	425.0	106.3	153.5	16.5	852.1	887.1	91	65.20	3

Overview

Variables

Interactions

Correlations

Pearson's r

Spearman's ρ

Kendall's τ

Phik (φk)

Missing values

Sample

First rows

Last rows

Duplicate rows

Most frequent